Table 1
Comparison of the mean lensing optical depth and the expected number of detected multiply imaged quasars for different values of the survey angular resolution corresponding to a perfect survey (θmin = 0′′), Gaia (θmin = 0.2′′), and typical ground-based observations (θmin = 0.6′′).
| Survey | NQSO | θmin = 0′′ | θmin = 0.2′′ | θmin = 0.6′′ | ||||
| Early-type galaxies | ||||||||
|
|
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| SIS | SIE | SIS | SIE | SIS | SIE | |||
|
|
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| ⟨τ⟩ | – | 3.994 × 10-3 | 3.747 × 10-3 | 3.917 × 10-3 | 3.663 × 10-3 | 2.718 × 10-3 | 2.431 × 10-3 | |
| ⟨τ2⟩ / ⟨τ⟩ | – | – | 0.917 | – | 0.92 | – | 0.948 | |
| ⟨τ3⟩ / ⟨τ⟩ | – | – | 1.15 × 10-3 | – | 2.564 × 10-2 | – | 4.614 × 10-2 | |
| ⟨τ4⟩ / ⟨τ⟩ | – | – | 8.205 × 10-2 | – | 5.25 × 10-2 | – | 5.59 × 10-3 | |
|
|
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| This study | 6.64465 × 105 | 2653 | 2490 | 2602 | 2433 | 1806 | 1615 | |
| Three images | – | – | 3 | – | 62 | – | 75 | |
| Four images | – | – | 204 | – | 134 | – | 9 | |
| Late-type galaxies | ||||||||
|
|
||||||||
| SIS | SIE | SIS | SIE | SIS | SIE | |||
|
|
||||||||
| ⟨τ⟩ | – | 1.278 × 10-3 | 1.141 × 10-3 | 8.404 × 10-4 | 6.815 × 10-4 | – | – | |
| ⟨τ2⟩ / ⟨τ⟩ | – | – | 0.8413 | – | 0.92 | – | – | |
| ⟨τ3⟩ / ⟨τ⟩ | – | – | 0.01206 | – | 0.07244 | – | – | |
| ⟨τ4⟩ / ⟨τ⟩ | – | – | 0.1466 | – | 0.05192 | – | – | |
|
|
||||||||
| This study | 6.64465 × 105 | 849 | 758 | 558 | 453 | – | – | |
| Three images | – | – | 9 | – | 33 | – | – | |
| Four images | – | – | 111 | – | 24 | – | – | |
| All deflectors (early- and late-type galaxies) | ||||||||
|
|
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| SIS | SIE | SIS | SIE | SIS | SIE | |||
|
|
||||||||
| This study | 6.64465 × 105 | 3502 | 3248 | 3160 | 2886 | 1806 | 1615 | |
| > two images | – | – | 327 | – | 253 | – | 84 | |
|
|
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| Mignard (2012) | 5.5−7 × 105 | |||||||
| Slezak (2007) | 7.2 × 105 | |||||||
Notes. For each value of θmin, the table displays the average lensing optical depth ⟨τ⟩ for both the SIS and SIE cases. In the latter case, the fraction of lensing events as a function of the number i of lensed images detected is also displayed ⟨τi⟩ / ⟨τ⟩. The bottom part of the table indicates the expected number of lenses in the survey, the total number, and the number of events with a given number of detected lensed images. For comparison, we report the expected number of lensing events considering the population of sources found in Mignard (2012) and Slezak (2007), assuming that these sources have a similar distribution in the redshift-absolute magnitude diagram.
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